InterviewSolution

Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

51.	Previous probabilities in Bayes Theorem that are changed with the new available information are called __________(a) independent probabilities(b) dependent probabilities(c) interior probabilities(d) posterior probabilitiesThe question was posed to me in an online interview.The doubt is from Bayes Theorem in portion Probability of Mathematics – Class 12
Answer» Right option is (d) posterior probabilities For explanation I WOULD say: In Bayesian statistics, we calculate new PROBABILITY after information becomes available due to new events and this is KNOWN as Posterior Probability. There is no term LIKE Independent probabilities and DEPENDENT probabilities, there are only independent events and dependent events. Interior probabilities represent probabilities of the intersection between two events.

52.	The term Bernoulli trials is termed after which swiss mathematician?(a) Jacob Bernoulli(b) Albert Einstein(c) Johann Gutenberg(d) ArchimedesThe question was posed to me in a national level competition.My doubt is from Bernoulli Trials and Binomial Distribution in division Probability of Mathematics – Class 12
Answer» The correct OPTION is (a) Jacob Bernoulli Easy EXPLANATION: Bernoulli trials is termed after swiss MATHEMATICIAN Jacob Bernoulli. Bernoulli trials is also CALLED a DICHOTOMOUS experiment and is repeated n times. If in each trial the probability of success is constant, then such trials are called Bernoulli trails.

53.	A bag contains 3 red, 2 white and 4 green balls. What is the probability of drawing the second ball to be white and the first ball drawn is green? The balls are replaced in the bag.(a) \(\frac {1}{9}\)(b) \(\frac {2}{9}\)(c) \(\frac {8}{81}\)(d) \(\frac {2}{81}\)I had been asked this question in an online quiz.My question is based upon Probability topic in division Probability of Mathematics – Class 12
Answer» Right choice is (c) \(\frac {8}{81}\) For explanation I WOULD say: TOTAL number of balls = 9 The probability of the first ball to be WHITE = \(\frac {2}{9}\) The probability of drawing green ball for the second time with REPLACEMENT = \(\frac {4}{9}\) Total probability = \(\frac {2}{9} \times \frac {4}{9} = \frac {8}{81}\)

54.	A bag contains 4 red and 7 blue balls. What is the probability of drawing a red ball if the first ball drawn is blue? The balls drawn are not replaced in the bag.(a) \(\frac {7}{11}\)(b) \(\frac {7}{10}\)(c) \(\frac {4}{10}\)(d) \(\frac {9}{11}\)I got this question in a job interview.I need to ask this question from Multiplication Theorem on Probability in chapter Probability of Mathematics – Class 12
Answer» Correct CHOICE is (c) \(\frac {4}{10}\) Easy explanation: Total number of balls = 4 + 7 = 11 The PROBABILITY of the FIRST ball to be BLUE = \(\frac {7}{11}\) The probability of drawing red ball as the second ball out without replacement = \(\frac {4}{10}\)

55.	A bag contains 4 red and 7 blue balls. What is the probability of drawing a blue ball if the first ball drawn is red? The balls drawn are not replaced in the bag.(a) \(\frac {7}{10}\)(b) \(\frac {8}{10}\)(c) \(\frac {7}{1}\)(d) \(\frac {4}{11}\)I have been asked this question during an online exam.This interesting question is from Multiplication Theorem on Probability topic in division Probability of Mathematics – Class 12
Answer» The correct option is (a) \(\frac {7}{10}\) To explain I would SAY: Total number of balls = 4 + 7 = 11 The probability of the first ball to be red = \(\frac {4}{11}\) The probability of drawing BLUE ball as the second ball out without replacement = \(\frac {7}{10}\)

56.	If P(A) = 7/11, P(B) = 6 / 11 and P(A∪B) = 8/11, then P(A\|B) = ________(a) 3/5(b) 2/3(c) 1/2(d) 1I had been asked this question in an international level competition.The question is from Conditional Probability in chapter Probability of Mathematics – Class 12
Answer» RIGHT option is (d) 1 Explanation: We know that P(A\|B) = P(A∩B) / P(B). (By formula for conditional PROBABILITY) ALSO P(A∪B) = P(A)+P(B) – P(A∩B). (By formula of probability) \(\RIGHTARROW\) 8/11 = 7/11 + 6/11 – P(A∩B) \(\Rightarrow\) P(A∩B) = 13/11 – 7/11 \(\Rightarrow\) P(A∩B) = 6/11 P(A\|B) = (6/11) / (6/11). P(A\|B) = 1.

57.	Bernoulli trials are also called as _____ or _____ questions.(a) positive, negative(b) natural, whole(c) yes, no(d) mutually exclusive, mutually inclusiveI have been asked this question in an online quiz.I want to ask this question from Bernoulli Trials and Binomial Distribution topic in portion Probability of Mathematics – Class 12
Answer» The correct option is (c) yes, no For explanation I WOULD say: Bernoulli trials is also CALLED a DICHOTOMOUS experiment and is repeated N times. Bernoulli trials is also called as a ‘yes’ or ‘no’ questions because it has only TWO outcomes, those are ‘success’ and ‘failure’.

58.	What is the probability of obtaining 4 heads in a row when a coin is tossed?(a) \(\frac {5}{8}\)(b) \(\frac {6}{19}\)(c) \(\frac {1}{16}\)(d) \(\frac {4}{7}\)I got this question during a job interview.I'd like to ask this question from Probability topic in portion Probability of Mathematics – Class 12
Answer» The correct option is (c) \(\FRAC {1}{16}\) EASIEST explanation: Probability of getting 4 heads in a row = \(\frac {1}{2} \times \frac {1}{2} \times \frac {1}{2} \times \frac {1}{2} = \frac {1}{16}\) HENCE, the probability of getting 4 heads in a row = \(\frac {1}{16}\)

59.	(n-x) is the number of successes in a binomial distribution.(a) False(b) TrueI got this question by my college professor while I was bunking the class.This key question is from Bernoulli Trials and Binomial Distribution in chapter Probability of Mathematics – Class 12
Answer» Correct choice is (a) False For explanation: Formula for BINOMIAL DISTRIBUTION is P [X = x] = ^nCxp^x q^N-x Where n is the number of trials, x is the number of successes and (n-x) is FAILURES.

60.	A bag contains 4 red and 7 blue balls. What is the probability of drawing a red ball if the first ball drawn is blue? The balls drawn are replaced in the bag.(a) \(\frac {4}{11}\)(b) \(\frac {8}{11}\)(c) \(\frac {4}{18}\)(d) \(\frac {14}{11}\)This question was posed to me during an online interview.I need to ask this question from Multiplication Theorem on Probability in chapter Probability of Mathematics – Class 12
Answer» Correct choice is (a) \(\frac {4}{11}\) The EXPLANATION: TOTAL number of BALLS = 4 + 7 = 11 The probability of the first ball to be blue = \(\frac {7}{11}\) The probability of drawing red ball as the second ball out without replacement = \(\frac {4}{11}\)

61.	A dice is thrown twice, what is the probability of getting two 3’s?(a) \(\frac {1}{66}\)(b) \(\frac {1}{16}\)(c) \(\frac {1}{36}\)(d) \(\frac {1}{36}\)The question was posed to me in final exam.I'd like to ask this question from Probability topic in portion Probability of Mathematics – Class 12
Answer» The correct OPTION is (d) \(\frac {1}{36}\) To ELABORATE: PROBABILITY of GETTING 3 in the first throw = \(\frac {1}{6}\) Probability of getting of 3 in the second throw = \(\frac {1}{6}\) Total probability = \(\frac {1}{6} \times \frac {1}{6} = \frac {1}{36}\)

62.	A bag contains 9 identical balls, of which are 4 are blue and 6 are green. Three balls are taken out randomly from the bag after one another. Find the probability that all three balls are blue?(a) \(\frac {5}{8}\)(b) \(\frac {6}{19}\)(c) \(\frac {5}{21}\)(d) \(\frac {4}{7}\)The question was posed to me in examination.I would like to ask this question from Multiplication Theorem on Probability in chapter Probability of Mathematics – Class 12
Answer» Right choice is (c) \(\frac {5}{21}\) For explanation I would say: Since6 balls are green, the probability of first ball to be DRAWN is green = \(\frac {6}{9}\) The probability of the first ball to be green, 8 balls are left and 5 out of them are green = \(\frac {5}{8}\) If the first two balls are green, then the probability of the THIRD ball to be green = \(\frac {4}{7}\) According to multiplication theorem, \(\frac {6}{9} . \frac {5}{8} . \frac {4}{7} = \frac {5}{21}\)

63.	A dice is thrown, what is the probability of getting multiples of 2?(a) 1/8(b) 1/6(c) 1/2(d) 1/3The question was asked in an internship interview.The origin of the question is Random Variables and its Probability Distributions in division Probability of Mathematics – Class 12
Answer» CORRECT choice is (c) 1/2 The EXPLANATION: Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6} Multiples of 2 = {2, 4, 6} Total probability = \(\FRAC {number \, of \, multiples \, of \, 3}{number \, of \, possible \, outcomes} = \frac {3}{6}=\frac {1}{2}\)